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![[parent]](http://images.planetmath.org:8080/images/uparrow.png)
Collatz tree
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(Data Structure)
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A Collatz tree or Collatz graph is a tree representation of several Collatz sequences joined together at their common terms the closer they are to the root term, which is 1. Typically the powers of 2 are placed in the central column, though placing to the left or the right are also viable options. In the
following illustration, given to a height of 12, the powers of 2 are placed in the rightmost column:
- 1
- J. C. Lagarias, ``The
 problem and its generalizations'', Amer. Math. Monthly, 92 (1985): 3 - 23
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"Collatz tree" is owned by PrimeFan.
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(view preamble)
| Other names: |
Collatz graph |
This object's parent.
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Cross-references: height, right, column, root, terms, Collatz sequences, representation, tree
There are 3 references to this entry.
This is version 1 of Collatz tree, born on 2007-02-22.
Object id is 8954, canonical name is CollatzTree.
Accessed 764 times total.
Classification:
| AMS MSC: | 11B37 (Number theory :: Sequences and sets :: Recurrences) |
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Pending Errata and Addenda
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![$\displaystyle \begin{xy} *!C\xybox{ \xymatrix{ 96\ar[d] & 17\ar[dr] & 104\ar[d]... ... & & 4\ar[d] \ & & & & & & & & & 2\ar[d] \ & & & & & & & & & 1 } } \end{xy}$](http://images.planetmath.org:8080/cache/objects/8954/l2h/img1.png "$\displaystyle \begin{xy} *!C\xybox{ \xymatrix{ 96\ar[d] & 17\ar[dr] & 104\ar[d]... ... & & 4\ar[d] \ & & & & & & & & & 2\ar[d] \ & & & & & & & & & 1 } } \end{xy}$")